Method of decoding a current image

ABSTRACT

The present invention relates to an image processing technique, and in particular to a method for restoring a compressed image by using a hybrid motion compensation discrete cosine transform (hybrid MC/DCT) mechanism, including: a step of defining a smoothing functional having a smoothing degree of an image and reliability for an original image by pixels having an identical property in image block units; and a step of computing a restored image by performing a gradient operation on the smoothing functional in regard to the original image, thereby preventing the blocking artifacts and the ringing effects in regard to the pixels having an identical property in image blocks.In one embodiment, the method includes obtaining a pixel value in a current block and at least one adjacent pixel value according to a smoothing direction, and obtaining a smoothing value of the current image based on the obtained pixel value in the current block and the adjacent pixel value according to the smoothing direction. A pixel value around a boundary of the current block is smoothed based on the smoothing value.

DIVISIONAL REISSUE APPLICATIONS

Notice: More than one reissue application has been filed for the reissueof U.S. Pat. No. 6,611,361. The other reissue applications areapplication Ser. Nos. 11/212,137, 11/808,423, 11/892,177, 11/892,178,and 11/892,176.

DOMESTIC PRIORITY INFORMATION

This is a direct divisional of application Ser. No. 11/212,137, filedAug. 26, 2005; the entire contents of which are hereby incorporated byreference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an image process technique, and inparticular to a method for restoring a compressed image by using ahybrid motion compensation discrete cosine transform (hybrid MC/DCT)mechanism, and an apparatus therefor.

2. Description of the Background Art

In general, image compression techniques, such as MPEG1 and MPEG2 employa hybrid motion compensation discrete cosine transform (hereinafter,referred to as “hybrid MC/DCT”) mechanism in order to improvecompression efficiency. The hybrid MC/DCT mechanism is roughly dividedinto an encoding process and a decoding process. In the encodingprocess, an original image is divided into a plurality of blocks inorder to compress information in a spatial section, a second-dimensionaldiscrete cosine transform is performed on each block, and redundancyinformation in the image or between the images is reduced by using thecorrelation on a time axis among the images in order to decreaseinformation in a temporal section. In the decoding process, the steps ofthe encoding process are performed in a reverse order. An encoder and adecoder are necessary to carry out the hybrid MC/DCT mechanism.

FIG. 1 is a block diagram illustrating an image encoder according to arelated art. As shown therein, an input image signal is subtracted froman image signal moved from and compensated by an image memory 9, passedthrough a first switching unit 2, and inputted to a DCT unit 3. The DCTunit 3 performs a discrete cosine transform on the inputted imagesignal. A quantization unit 4 quantizes the image signal, and outputs aDCT coefficient (q). An inverse quantization unit 6 inversely quantizesthe DCT coefficient (q), and an inverse DCT unit 7 carries out aninverse discrete cosine transform thereon, thereby restoring theoriginal image signal. The restored image signal is added to an imagesignal restored in a previous stage by an adder 8, and inputted to animage memory 9. A controller 5 controls switching of the first andsecond switching units 2, 10, and transmits INTRA/INTER information(p=mtype; flag for INTRA/INTER), transmission information (t; flag fortransmitted or not), and quantization information (qz=Qp; quantizerindication) to a decoder (not shown in FIG. 1). The image memory 9outputs a motion vector information (v=MV; motion vector) to thedecoder. The DCT unit 3 outputs the DCT coefficient (q) to the decoder.

However, information of the original image signal is lost during theprocess of coding the image signal described above, especially duringthe quantization process, thereby causing blocking artifacts and ringingeffects to the image which is reconstructed in the decoder. The blockingartifacts imply irregularity between the blocks generated due toinformation loss resulting from the quantization of the low-frequencyDCT coefficients, and the ringing effects result from quantizationerrors of the high-frequency DCT coefficients.

That is, in accordance with a coding technique using the DCT in a codingsystem of a static image or dynamic image, an image is divided into aplurality of blocks, and the DCT is performed on each block. On theother hand, when the DCT is carried out on the original image, itsimportant information is mainly included in low-frequency elements, andbecomes lesser in high-frequency elements. Furthermore, thelow-frequency elements include a lot of information relating to adjacentblocks. The DCT does not consider the correlation between the blocks,and quantizes the low-frequency elements by blocks, thereby destroyingcontinuity of the adjacent blocks. It is called the blocking artifacts.

In addition, when the coefficients obtained by performing the DCT arequantized, as a quantization interval is increased, the elements to becoded are decreased, and thus the number of the bits to be processed isreduced. As a result, the information of the high-frequency elementincluded in the original image is reduced, thereby generating distortionof the reconstructed image. It is called the ringing effects. Theringing effects generated by increasing the quantization interval areserious especially in a contour of an object in the reconstructed image.

As techniques for removing the blocking artifacts and the ringingeffects, employed are a low pass filtering method and a regularizedimage restoration method.

According to the low pass filtering method, a plurality of pixels arounda predetermined pixel are selected, and an average value thereof iscomputed. Here, a filter tap or filter coefficients are set byexperience. For example, referring to FIG. 2, there is provided a blockof N*N size. Reference numerals A to F depict pixels. Pixels C, D areadjacent to a boundary of the block. In order to reduce irregularvariations between the pixels C, D, a k-tap (here, 7-tap) filtering isperformed, and a threshold value replacing a D pixel value is computedaccording to local statistics. There is an advantage in that acomputation amount is reduced by utilizing a predetermined thresholdvalue according to the comparison with the local statistics. However, anadaptive processing power in accordance with a quantization parameter isdeficient, and thus a screen quality of the restored image isexcessively smoothed according to the kind of the images and compressionratio.

The regularized image restoration method adaptively deals with theblocking artifacts in accordance with statistical properties of theimage. That is, irregular information around the boundary of the blockor in the block is all computed. However, the computed values form amatrix shape, and thus a real time processing is difficult due to thegreat computation amount. In addition, an average value obtained by acomputation result of the irregular information is equally applied tothe pixels, regardless of a degree of irregularity. Accordingly, when ablock has a high degree of irregularity, it can be reduced. However, incase of a block having a low degree of irregularity, it may beincreased. Thus, the system is not adaptive. Also, the information inthe temporal section is not processed, and thus irregularity between theimages cannot be adaptively processed.

SUMMARY OF THE INVENTION

It is therefore an object of the present invention to provide a methodfor restoring a compressed image of an image processing system and anapparatus therefor which can reduce the blocking artifacts and ringingeffects generated in a restored image signal.

It is another object of the present invention to provide a method forrestoring a compressed image of an image processing system and anapparatus therefor which consider a smoothing degree of an image andreliability for an original image by pixels having an identical propertyin image block units, during a decoding process.

In order to achieve the above-described objects of the presentinvention, there is provided a method for restoring a compressed imageof an image processing system including: a step of defining a smoothingfunctional having a degree of smoothing an image and reliability for anoriginal image by pixels having an identical property in image blockunits; and a step of computing a restored image by performing a gradientoperation on the smoothing functional in regard to the original image.

These and other objects of the present application will become morereadily apparent from the detailed description given hereinafter.However, it should be understood that the detailed description andspecific examples, while indicating preferred embodiments of theinvention, are given by way of illustration only, since various changesand modifications within the spirit and scope of the invention willbecome apparent to those skilled in the art from this detaileddescription.

The present invention relates to a method of decoding a current image.

In one embodiment, the method includes obtaining a pixel value in acurrent block and at least one adjacent pixel value according to asmoothing direction, and obtaining a smoothing value of the currentimage based on the obtained pixel value in the current block and theadjacent pixel value according to the smoothing direction. A pixel valuearound a boundary of the current block is smoothed based on thesmoothing value. For example, in one embodiment, the smoothing directionincludes at least one of temporal direction and spatial direction.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will become better understood with reference tothe accompanying drawings which are given only by way of illustrationand thus are not limitative of the present invention, wherein:

FIG. 1 is a block diagram illustrating an image encoder according to arelated art;

FIG. 2 illustrates pixels in order to explain a low pass filteringmethod carried out in the image encoder of FIG. 1; FIG. 3 is a blockdiagram illustrating an apparatus for restoring a compressed image of animage processing system in accordance with an embodiment of the presentinvention;

FIG. 4 illustrates an example of a configuration of original pixels in ablock of an original image in accordance with the present invention;

FIG. 5 illustrates directions of the irregular smoothing degree of thepixels in accordance with the present invention;

FIG. 6 illustrates an image moved and compensated in regard to atemporal section in accordance with the present invention; and

FIG. 7 illustrates a flowchart of the apparatus for restoring thecompressed image of the image processing system in accordance with anembodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 3 is a block diagram illustrating an apparatus for restoring acompressed image of an image processing system in accordance with thepresent invention. As shown therein, a decoder 210 receives INTRA/INTERinformation (p=mtype), transmission information (t), quantizationinformation (qz=Qp), a discrete cosine transform (DCT) coefficient (q)and motion vector information (v=MV; motion vector) from an encoder (asdepicted in FIG. 1), and performs decoding. The encoder and the decoder210 are connected by a communication channel or network. A postprocessing unit 220 receives image signals Y, U, V, a quantizationvariable (qz=Qp), a macro block type (mtype) and a motion vector (v=MV)from the decoder 210, and carries out an operation of restoring thecompressed image in accordance with the present invention.

According to the present invention, a smoothing functional is defined inregard to pixels having an identical property by blocks, aregularization parameter is computed based on the smoothing functional,and available values are applied to the regularization parameter,thereby obtaining an image to be restored. Thereafter, an iterativetechnique, a discrete cosine transform (DCT), a projection and aninverse DCT are sequentially performed on the obtained image, therebyrestoring a similar image to the original image. The whole processeswill now be described in detail.

Definition of Smoothing Functional

When an original image (f) is compressed and transmitted, an image (g)reconstructed in the decoder 210 is represented by the followingequation.g=f+n   (1)

Here, “g” and “f” indicate row vectors re-arranged in a stack-order,namely a scanning order, and “n” indicates a quantization error. When itis presumed that a size of the image is M×M, the original image (f), thereconstructed image (g) and (n) are column vectors having a size of M×1.

An original pixel for the original image (f) is represented by f(i,j).Here, “i” and “j” indicate a position of the pixel in the image.

FIG. 4 illustrates configuration of the original pixels f(i,j) in theblock of the original image (f) in order to explain the presentinvention. Reference numerals in FIG. 4 depict information of therespective pixels. 8×8 pixels are shown in a single block.

The 8×8 pixels in the block are classified into the pixels having anidentical property. That is, the pixels are divided in accordance withtheir position, vertical direction, horizontal direction and smoothingvariation in the temporal section. Accordingly, it is defined that a setof the pixels positioned at a boundary of the block in a verticaldirection is C_(VB), a set of the pixels positioned inside the block inthe vertical direction is C_(VW), a set of the pixels positioned at aboundary of a block in a horizontal direction is C_(HB), a set of thepixels positioned inside the block in the horizontal direction isC_(HW), and a set of the pixels moved and compensated in the temporalsection is C_(T). The sets C_(VB), Chd VW, C_(HB), C_(HW), C_(T) arerepresented by the following expressions.C_(VB)={f(i,j): i mod 8=0,1, and j=0,1, . . . , M−1}C_(VW)={f(i,j): i mod 8=0,1, and j=0,1, . . . , M−1}  (2)C_(HB)={f(i,j): i mod 8=0,1, and i=0,1, . . . M−1}C_(HW)={f(i,j): j mod 8=0,1, and i=0,1, . . . , M=1}C_(T)={f(i,j): f(i,j)εMB_(inter) or f(i,j)εMB_(not coded)}

Here, the set C_(T) is a set of the pixels having a macro block type of“inter” or “not coded” in order to remove temporal redundancyinformation.

The smoothing functional M(f) for using the regularization restorationmethod from the above-defined sets C_(VB), C_(VW), C_(HB), C_(HW), C_(T)is defined as follows.M(f)=M_(VB)(f)+M_(HB)(f)+M_(VW)(f)+M_(HW)(f)+M_(T)(f)   (3)

Here, M_(VB)(f) is a smoothing functional for the set C_(VB), M_(HB)(f)is a smoothing functional for C_(HB), M_(VW)(f) is a smoothingfunctional for the set C_(VW), M_(HW)(f) is a smoothing functional forthe set C_(HW), and M_(T)(f) is a smoothing functional for the setC_(T). The smoothing fuctionals are respectively defined as follows.

 M_(VB)(f)=∥Q_(VB)f∥²+α_(VB)∥g−f∥² _(w1)M_(HB)(f)=∥Q_(HB)f∥²+α_(HB)∥g−f∥² _(w2)M_(VW)(f)=∥Q_(VW)f∥²+α_(VW)∥g−f∥² _(w3)M_(HW)(f)=∥Q_(HW)f∥²+α_(HW)∥g−f∥² _(w4)M_(T)(f)=∥Q_(T)f∥²+α_(T)∥g−f∥² _(w5)

Here, first terms in each expression indicate a smoothing degree for theoriginal pixel (reference pixel) and adjacent pixel, and second termsindicate reliability for the original pixel and the restored pixel.“∥.∥” indicates the Euclidean norm. Q_(VB), Q_(VW), Q_(HB), Q_(HW),Q_(T) indicate high pass filters for smoothing the pixels in the setsC_(VB), C_(VW), C_(HB), C_(HW), C_(T).

The first term at the right side is represented by the followingexpression. $\begin{matrix}{{{{{Q_{VB}f}}^{2} = {\sum\limits_{n = 0}^{M - 1}\quad{\sum\limits_{m}\quad\left( {{f\left( {m,n} \right)} - {f\left( {{m - 1},n} \right)}} \right)^{2}}}},\quad{m = 0},8,16,\ldots}{{{{Q_{HB}f}}^{2} = {\sum\limits_{n}\quad{\sum\limits_{m = 0}^{M - 1}\quad\left( {{f\left( {m,n} \right)} - {f\left( {m,{n - 1}} \right)}} \right)^{2}}}},\quad{n = 0},8,16,\ldots}{{{{Q_{VW}f}}^{2} = {\sum\limits_{n = 0}^{M - 1}\quad{\sum\limits_{m}\quad\left( {{f\left( {m,n} \right)} - {f\left( {{m - 1},n} \right)}} \right)^{2}}}},\quad{m \neq 0},8,16,\ldots}{{{{Q_{HW}f}}^{2} = {\sum\limits_{n}\quad{\sum\limits_{m = 0}^{M - 1}\quad\left( {{f\left( {m,n} \right)} - {f\left( {m,{n - 1}} \right)}} \right)^{2}}}},\quad{n \neq 0},8,16,\ldots}{{{Q_{T}f}}^{2} = {\sum\limits_{n}\quad{\sum\limits_{m}\quad\left( {{f_{MC}\left( {m,n} \right)} - {f\left( {m,n} \right)}} \right)^{2}}}}} & (5)\end{matrix}$

The smoothing functionals represented by Expression (4) are quadraticequations, respectively. Thus, local minimizers of each smoothingfunctional become global minimizers.

FIG. 5 illustrates directions of the irregular smoothing degree of thepixels. There are a single pixel at the center and eight pixelstherearound. There are also shown horizontal and vertical arrowsstarting from the pixel at the center. The arrows respectively depictthe directions of the irregular smoothing degree in regard to the fouradjacent pixels. That is to say, the irregular smoothing degree isconsidered in four directions in respect of a single pixel.

FIG. 6 illustrates an image moved and compensated in regard to thetemporal section in accordance with the present invention. Arrows depictthe correlation of a currently-restored image with a previously-restoredimage and a succeedingly reconstructed image, respectively.

α_(VB), α_(HB), α_(VW), α_(HW), α_(T) included in the second terms ofExpression (4) are regularization parameters in regard to each set,indicate a ratio of the smoothing degree and reliability, and imply anerror element. W1, W2, W3, W4, W5 indicate diagonal matrixes having asize of M×M in order to determine whether each set has an element, andhave a value of “1”, or “0” according to whether each pixel is includedin a corresponding set. That is, if the respective pixels are includedin the corresponding sets, the value of the diagonal elements is “0”. Ifnot, the value of the diagonal elements is

Thereafter, the regularization parameters, α_(VB), α_(HB), α_(VW),α_(HW), α_(T) are approximated as follows.

Approximation of Regularization Parameters

Approximation of the regularization parameters is a major elementdetermining performance of the smoothing functional. In order to reducethe computation amount, presumptions are made as follows.

-   (1) A maximum value of the quantization error generated in the    quantization process of the DCT region is Q_(p), and thus it is    presumed that the quantization variables Q_(p) are regular in each    macro block. For this, the maximum quantization error of the DCT    coefficients of each macro block is regularly set to be Qp.-   (2) It is also presumed that the DCT quantization errors have the    Gaussain distribution property in the spatial section. Under the    above presumptions, in case a set theoretic is    applied, each regularization parameter is approximated as follows.    $\begin{matrix}    {{\alpha_{VB} = {\frac{{{Q_{VB}f}}^{2}}{{{g - f}}_{W1}^{2}}\quad = {\frac{{{Q_{VB}g}}^{2}}{{{g - f}}_{W1}^{2}} = \frac{{{Q_{VB}g}}^{2}}{\sum\limits_{n}\quad{\sum\limits_{m}\quad{{w_{1}\left( {m,n} \right)}{{Qp}^{2}\left( {m,n} \right)}}}}}}}{\alpha_{HB} = {\frac{{{Q_{HB}f}}^{2}}{{{g - f}}_{W2}^{2}} = {\frac{{{Q_{HB}g}}^{2}}{{{g - f}}_{W2}^{2}} = \frac{{{Q_{HB}g}}^{2}}{\sum\limits_{n}\quad{\sum\limits_{m}\quad{{w_{2}\left( {m,n} \right)}{{Qp}^{2}\left( {m,n} \right)}}}}}}}\quad{\alpha_{VW} = {\frac{{{Q_{VW}f}}^{2}}{{{g - f}}_{W3}^{2}}\quad = {\frac{{{Q_{VW}g}}^{2}}{{{g - f}}_{W3}^{2}} = \frac{{{Q_{VW}g}}^{2}}{\sum\limits_{n}\quad{\sum\limits_{m}\quad{{w_{3}\left( {m,n} \right)}{{Qp}^{2}\left( {m,n} \right)}}}}}}}\quad{\alpha_{HW} = {\frac{{{Q_{HW}f}}^{2}}{{{g - f}}_{W4}^{2}}\quad = {\frac{{{Q_{HW}g}}^{2}}{{{g - f}}_{W4}^{2}} = \frac{{{Q_{HW}g}}^{2}}{\sum\limits_{n}\quad{\sum\limits_{m}\quad{{w_{4}\left( {m,n} \right)}{{Qp}^{2}\left( {m,n} \right)}}}}}}}\quad{\alpha_{T} = {\frac{{{Q_{T}f}}^{2}}{{{g - f}}_{W5}^{2}}\quad = {\frac{{{Q_{T}g}}^{2}}{{{g - f}}_{W5}^{2}} = \frac{{{Q_{T}g}}^{2}}{\sum\limits_{n}\quad{\sum\limits_{m}\quad{{w_{5}\left( {m,n} \right)}{{Qp}^{2}\left( {m,n} \right)}}}}}}}} & (6)    \end{matrix}$

Here, Q² _(p)(m,n) is a quantization variable of a macro block includinga (m,n)th pixel of a two-dimensional image.

In Expression (6), denominator terms of the respective regularizationparameters are a sum of the energy for the quantization noise of theelements included in each group. As described above, the values of theregularization parameters may be easily computed by applying the settheoretic under the two presumptions.

Computing Pixels to be Restored From Smoothing Functional

Only the original image needs to be computed. However, the smoothingfunctional includes a square term of the original image. Accordingly, inorder to compute the original image, a gradient operation is carried outon the smoothing functional in regard to the original image. A resultvalue thereof is “0”, and represented by the following expression.∇_(f)M(f)=2Q^(T) _(VB)Q_(VB)+2Q^(T) _(HB)Q_(HB)+2Q^(T) _(VW)Q_(VW)+2Q^(T) _(HW)Q_(HW)+2Q^(T)TQ_(T)−2α_(VB)W^(T) ₁W₁(g−f)−2α_(HB)W^(T) ₂W₂(g−f)−2α_(VW)W^(T) ₃W₃(g−f)−2α_(HW)W^(T) ₄W₄(g−f)−2α_(T)(g−f)=0   (7)

Here, a superscript “T” indicates a transposition of the matrix.

A restored image similar to the original image (f) can be obtained byExpression (7). However, operation of an inverse matrix must beperformed, and thus the computation amount is increased. Thus, inaccordance with the present invention, the restored image is computed byan iterative technique which will now be explained.

Iterative Technique

When Expression (7) is iterated k times, an iterative solution f_(k+1)is represented by the following expression.f_(k+1)=f_(k)+β[Ag−Bf_(k)],A=α_(VB)W₁+α_(HB)W₂+α_(VW)W₃+α_(HW)W₄+α_(T)W₅   (8)B=(Q^(T) _(VB)Q_(VB)+Q^(T) _(HB)Q_(HB)+Q^(T) _(VW)Q_(VW)+Q^(T)_(HW)Q_(HW)+Q^(T) _(T)Q_(T))+A

In Expression (8), “β” is a relaxation parameter having a convergenceproperty. Expression (8) can be represented by the following expressionby computing consecutive iterative solutions.(f_(k+1)−f_(κ))=(I−B)(f_(k)−f_(k−1))   (9)

Here, “I” is an identity matrix, and the matrix B has a positivedefinite property. Therefore, when the following condition is satisfied,the iterative solutions are converged.∥I−B∥<1   (9)

Expression (10) can be summarized as follows. $\begin{matrix}{0 < \beta < \frac{2}{1 + {\max_{i}{\lambda_{i}(A)}}}} & (11)\end{matrix}$

In Expression (11), “λ(A)” depicts an eigen value of the matrix A. Aconsiderable amount of computation is required to compute the eigenvalue λ(A). However, the high pass filters have a certain shapedetermined according to the positions of the respective pixels,regardless of the image. Accordingly, before computing Expression (8),the eigen value λ(A) can be replaced by a fixed value. The value may becomputed by a power method which has been generally used ininterpretation of numerical values.

For example, a computation process of an eigen value of an iterativesolution will now be explained.x_(k+1)=Kx_(k)Here, “x_(k)” is a vector of M×1, and “K” is a positive-definitesymmetric M×M matrix. The eigen value λ′ of the matrix K is approximatedas follows.$\lambda^{\prime} = \frac{\left( x_{k + 1} \right)^{T}x_{k}}{\left( x_{k}^{T} \right)x_{k}}$

In the above expression, if “k” is to infinity, the eigen value λ′ isapproximated to a real value.

Thus, the iterative solution represented by Expression (8) is computed.The next thing to be considered is a time of finishing the iterativetechnique, in order to determine the number of iteration. Here, twostandards are set as follows.

Firstly, a predetermined threshold value is set before startingiteration, an image obtained after iteration, namely apartially-restored image is compared with the previously-set thresholdvalue, and it is determined whether the iteration technique iscontinuously performed according to a comparison result.

Secondly, the iteration technique is performed as many as apredetermined number, and then finished.

According to the first standard, a predetermined threshold value is setin performing iteration, and thus a wanted value is obtained. However,although the iteration number is increased, it may happen that thepredetermined threshold value is not reached. On the other hand, thesecond standard is performed by experience, but can reduce a computationamount. Therefore, the two standards may be selectively used accordingto the design specification.

FIG. 7 is a flowchart of the apparatus for restoring the compressedimage of the image processing system in accordance with the presentinvention. As shown therein, in the step S1, the quantization variableQp and the image signals Y, U, V are inputted, and the regularizationparameter is approximated as described above. In the step S2, thegradient operation is performed on the smoothing functional in regard tothe original image. In the step S3, an iterative solution, namely awanted restored image is obtained by the iteration technique. In thisstep, employed are the image signals Y, U, V and the motion vector MVwhich is moved and compensated.

In the step S4, the DCT is performed on the restored image correspondingto the iterative solution f_(k+1) obtained in the step S3. An (u,v)thDCT coefficient of the two-dimensional restored image is expressed asF_(k+1)(u,v), and must exist in the following section in accordance witha property of the quantization process.G(u,v)−Qp≦F_(k+1)(u,v)≦G(u,v)+Qp   (12)

Here, “Qp” is a maximum quantization error as explained above, and“G(u,v)” is a two-dimensional DCT coefficient obtained by performing theDCT on the reconstructed image (g). The DCT coefficients F_(k+1)(u,v)and G(u,v) are represented as follows. In Expression (13), “B” indicatesa block DCT.F_(k+1)(u,v)=(Bf_(k+1))(u,v), and G(u,v)=(Bg)(u,v)   (13)

In the step S6, a section of the DCT coefficient of the restored imageis set as in Expression (12). Accordingly, in case the DCT coefficientF_(k+1)(u,v) of the restored image is not in the predetermined section,it must be projected as follows. A projection process is carried out inthe step S7, and represented by Expression (14).P(F_(k+1)(u,v))=G(u,v)−Qp, if F_(k+1)(u,v)<G(u,v)−QpP(F_(k+1)(u,v))=G(u,v)+Qp, if F_(k+1)(u,v)>G(u,v)−Qp   14P(F_(k+1)(u,v))=F_(k+1)(u,v), otherwise.

Expression (14) will now be described.

When F_(k+1)(u,v) is smaller than G(u,v)−Qp, the projected restoredimage P(F_(k+1)(u,v)) is mapped to G(u,v)−Qp. In case F_(k+1)(u,v) isgreater than G(u,v)+Qp, the projected restored image P(F_(k+1)(u,v)) ismapped to G(u,v)+Qp. Otherwise, the projected restored imageP(F_(k+1)(u,v)) is mapped as it is.

In the step S8, the inverse DCT is performed on the mapped imageP(F_(k+1)(u,v)) in the spatial section. The finally restored image isrepresented by Expression (14).f_(k+1)=B^(T)PBf_(k+1)   (15)

Here, “B” indicates the DCT, “P” indicates mapping, and “B^(T)”indicates the inverse DCT.

The restored image is stored in a frame memory in the post processingunit 220 (Step S9). The post processing unit 220 performs motioncompensation based on the motion vector MV (Step S10). The motion andcompensation image is employed for generation of the regularizationparameter for a succeeding image and the iteration technique.

The post processing unit 220 outputs the restored motion andcompensation image as a video signal to a display (not shown) (StepS11).

As discussed earlier, the present invention can restrict a section ofthe restored image for the respective pixels by using the variousregularization parameters. In addition, the present invention preventsflickering which may occur in the dynamic image compression technique.

Consequently, the present invention adaptively prevents the blockingartifacts and the ringing effects for the pixels having an identicalproperty in image block units, and thus can be widely used for theproducts of the hybrid MC-DCT mechanism.

As the present invention may be embodied in several forms withoutdeparting from the spirit or essential characteristics thereof, itshould also be understood that the above-described embodiment is notlimited by any of the details of the foregoing description, unlessotherwise specified, but rather should be construed broadly within itsspirit and scope as defined in the appended claims, and therefore allchanges and modifications that fall within the meets and bounds of theclaims, or equivalences of such meets and bounds are therefore intendedto be embraced by the appended claims.

1. A method for restoring a compressed image of an image processing system, comprising: a step for defining a smoothing functional having a smoothing degree of an image and reliability for an original image by pixels having an identical property in image block units; and a step for computing a restored image by performing a gradient operation on the smoothing functional in regard to the original image; wherein the smoothing functional M(f) comprises a sum of a smoothing functional M_(VB)(f) for pixels positioned at the boundary of a block in a vertical direction, a smoothing functional M_(VW)(f) for pixels positioned inside the block in a horizontal direction, a smoothing functional M_(HB)(f) for pixels positioned at the boundary of a block in a horizontal direction, a smoothing functional M_(HW)(f) for pixels positioned inside the block in a horizontal direction, a smoothing functional M_(T)(f) for pixels moved and compensated in the temporal section, “f” indicating the original image.
 2. The method according to claim 1, wherein the step for defining the smoothing functional divides the pixels according to their position, horizontal direction, vertical direction and smoothing variation in a temporal section.
 3. The method according to claim 1, wherein the smoothing functionals M_(VB)(f), M_(HB)(f), M_(VW)(f), M_(HW)(f), M_(T)(f) are defined as; M_(VB)(f)=∥Q_(VB)f∥²+α_(VB)∥g−f∥² _(w1) M_(HB)(f)=∥Q_(HB)f∥²+α_(HB)∥g−f∥² _(w2) M_(VW)(f)=∥Q_(VW)f∥²+α_(VW)∥g−f∥² _(w3) M_(HW)(f)=∥Q_(HW)f∥²+α_(HW)∥g−f∥² _(w4) M_(T)(f)=∥Q_(T)f∥²+α_(T)∥g−f∥² _(w5) Q_(VB), Q_(VW), Q_(HB), Q_(HW), Q_(T) indicating high pass filters for smoothing the respective pixels, α_(VB), α_(VW), α_(HB), α_(HW), α_(T) being regularization parameters, g being a reconstructed image, and W1, W2, W3, W4, W5 indicating diagonal matrixes for determining whether each group has an element.
 4. The method according to claim 1, wherein the step for computing the restored image comprises a step for approximating the regularization parameter by applying a set theoretic, and it is presumed that the quantization variables of the DCT region regular in each macro block, and also presumed that the DCT quantization errors have the Gaussain distribution property in the spatial section.
 5. The method according to claim 4, wherein the regularization parameters are approximated as; $\alpha_{VB} = {\frac{{{Q_{VB}f}}^{2}}{{{g - f}}_{W1}^{2}}\quad = {\frac{{{Q_{VB}g}}^{2}}{{{g - f}}_{W1}^{2}} = \frac{{{Q_{VB}g}}^{2}}{\sum\limits_{n}\quad{\sum\limits_{m}\quad{{w_{1}\left( {m,n} \right)}{{Qp}^{2}\left( {m,n} \right)}}}}}}$ ${\alpha_{HB} = {\frac{{{Q_{HB}f}}^{2}}{{{g - f}}_{W2}^{2}} = {\frac{{{Q_{HB}g}}^{2}}{{{g - f}}_{W2}^{2}} = \frac{{{Q_{HB}g}}^{2}}{\sum\limits_{n}\quad{\sum\limits_{m}\quad{{w_{2}\left( {m,n} \right)}{{Qp}^{2}\left( {m,n} \right)}}}}}}}\quad$ ${\alpha_{VW} = {\frac{{{Q_{VW}f}}^{2}}{{{g - f}}_{W3}^{2}}\quad = {\frac{{{Q_{VW}g}}^{2}}{{{g - f}}_{W3}^{2}} = \frac{{{Q_{VW}g}}^{2}}{\sum\limits_{n}\quad{\sum\limits_{m}\quad{{w_{3}\left( {m,n} \right)}{{Qp}^{2}\left( {m,n} \right)}}}}}}}\quad$ ${\alpha_{HW} = {\frac{{{Q_{HW}f}}^{2}}{{{g - f}}_{W4}^{2}}\quad = {\frac{{{Q_{HW}g}}^{2}}{{{g - f}}_{W4}^{2}} = \frac{{{Q_{HW}g}}^{2}}{\sum\limits_{n}\quad{\sum\limits_{m}\quad{{w_{4}\left( {m,n} \right)}{{Qp}^{2}\left( {m,n} \right)}}}}}}}\quad$ $\alpha_{T} = {\frac{{{Q_{T}f}}^{2}}{{{g - f}}_{W5}^{2}}\quad = {\frac{{{Q_{T}g}}^{2}}{{{g - f}}_{W5}^{2}} = \frac{{{Q_{T}g}}^{2}}{\sum\limits_{n}\quad{\sum\limits_{m}\quad{{w_{5}\left( {m,n} \right)}{{Qp}^{2}\left( {m,n} \right)}}}}}}$ Q² _(p)(m,n) indicating a quantization variable of a macro block including an (m,n)th pixel of a two-dimensional image.
 6. The method according to claim 1, wherein a local minimizer of the smoothing functional is a global minimizer.
 7. The method according to claim 1, wherein the regularization parameter indicates a ratio of a smoothing degree of the image and reliability for the original image.
 8. The method according to claim 1, further comprising a step for computing an iterative solution in regard to a restored image, after computing the restored image.
 9. The method according to claim 8, wherein the iterative solution f_(k+1) is represented by; f_(k+1)=f_(k)+β[Ag−Bf_(k)], A=α_(VB)W₁+α_(HB)W₂+α_(VW)W₃+α_(HW)W₄+α^(T)W₅ B=(Q^(T) _(VB)Q_(VB)+Q^(T) _(HB)Q_(HB)+Q^(T) _(VW)Q_(VW)+Q^(T) _(HW)Q_(HW)+Q^(T) _(T)Q_(T))+A and, β is a relaxation parameter having a convergence property, and computed at the range of ${0 < \beta < \frac{2}{1 + {\max_{i}{\lambda_{i}(A)}}}},$  an eigen value λ(A) of the matrix A being replaced by a fixed value.
 10. The method according to claim 8, wherein a predetermined threshold value is set in computing an iterative solution, an image obtained after iteration is compared with the previously-set threshold value, and it is determined whether the iteration technique is continuously performed according to a comparison result, or the iteration is finished after the iteration technique is performed as many as a previously-set number.
 11. The method according to claim 8, further comprising a step for obtaining a mapped image by projecting a two-dimensional DCT coefficient of the restored image corresponding to a computed iterative solution, and for performing an inverse DCT on the mapped image.
 12. The method according to claim 11, wherein the step for obtaining the mapped image is mapping a projected restored image P(F_(k+1)(u,v)) to G(u,v)−Qp when the DCT coefficient of the restored image F_(k+1)(u,v) is smaller than G(u,v)−Qp, mapping the projected restored image P(F_(k+1)(u,v)) to G(u,v)+Qp when F_(k+1)(u,v) is greater than G(u,v)+Qp, and otherwise mapping the projected restored image P(F_(k+1)(u,v)) as it is, G(u,v) indicating a two-dimensional DCT coefficient obtained by performing the DCT on the reconstructed image, and Qp indicating quantization information.
 13. The method according to claim 1, wherein a predetermined threshold value is set in computing an iterative solution, an image obtained after iteration is compared with the previously-set threshold value, and it is determined whether the iteration technique is continuously performed according to a comparison result, or the iteration is finished after the iteration technique is performed as many as a previously-set number.
 14. The method according to claim 1, further comprising a step for obtaining a mapped image by projecting a two-dimensional DCT coefficient of the restored image corresponding to a computed iterative solution, and for performing an inverse DCT on the mapped image.
 15. The method according to claim 14, wherein the step for obtaining the mapped image is mapping a projected restored image P(F_(k+1)(u,v)) to G(u,v)−Qp when the DCT coefficient of the restored image F_(k+1)(u,v) is smaller than G(u,v)−Qp, mapping the projected restored image P(F_(k+1)(u,v)) to G(u,v)+Qp when F_(k+1)(u,v) is greater than G(u,v)+Qp, and otherwise mapping the projected restored image P(F_(k+1)(u,v)) as it is, G(u,v) indicating a two-dimensional DCT coefficient obtained by performing the DCT on the reconstructed image, and Qp indicating quantization information.
 16. An apparatus for restoring a compressed image of an image processing system, comprising: a decoder for decoding a coded image signal, and for outputting information of the restored image, such as the decoded image, a quantization variable, a macro block type and a motion vector; and a post processing unit for including the information of the . restored image inputted from the image decoder, for defining a smoothing functional including a sum of a smoothing functional M_(VB)(f) for pixels positioned at the boundary of a block in a vertical direction, a smoothing functional M_(VW)(f) for pixels positioned inside the block in a horizontal direction, a smoothing functional M_(HB)(f) for pixels positioned at the boundary of a block in a horizontal direction, a smoothing functional M_(HW)(f) for pixels positioned inside the block in a horizontal direction, a smoothing functional M_(T)(f) for pixels moved and compensated in the temporal section, “f” indicating the original image, and for performing a gradient operation on the smoothing functional in regard to the original image, the smoothing functional including a regularization parameter having weight of reliability for the original image.
 17. A method for restoring a compressed image of an image processing system, comprising: a step for defining a smoothing functional having a smoothing degree of an image and reliability for an original image by pixels having an identical property in image block units; a step for computing a restored image by performing a gradient operation on the smoothing functional in regard to the original image; and a step for computing an iterative solution in regard to the restored image, after computing the restored image.
 18. The method according to claim 17, wherein the step for defining the smoothing functional divided the pixels according to their position, horizontal direction, vertical direction and smoothing variation in a temporal section.
 19. The method according to claim 17, wherein the smoothing functional M(f) comprises a sum of a smoothing functional M_(VB)(f) for pixels positioned at the boundary of a block in a vertical direction, a smoothing functional M_(VW)(f) for pixels positioned inside the block in a horizontal direction, a smoothing functional M_(HB)(f) for pixels positioned at the boundary of a block in a horizontal direction, a smoothing functional M_(HW)(f) for pixels positioned inside the block in a horizontal direction, a smoothing functional M_(T)(f) for pixels moved and compensated in the temporal section, “f” indicating the original image.
 20. The method according to claim 19, wherein the smoothing functionals M_(VB)(f), M_(HB)(f), M_(VW)(f), M_(HW)(f), M_(T)(f) are defined as; M_(VB)(f)=∥Q_(VB)f∥²+α_(VB)∥g−f∥² _(w1) M_(HB)(f)=∥Q_(HB)f∥²+α_(HB)∥g−f∥² _(w2) M_(VW)(f)=∥Q_(VW)f∥²+α_(VW)∥g−f∥² _(w3) M_(HW)(f)=∥Q_(HW)f∥²+α_(HW)∥g−f∥² _(w4) M_(T)(f)=∥Q_(T)f∥²+α_(T)∥g−f∥² _(w5) Q_(VB), Q_(VW), Q_(HB), Q_(HW), Q_(T) indicating high pass filters for smoothing the respective pixels, α_(VB), α_(VW), α_(HB), α_(HW), α_(T) being regularization parameters, g being a reconstructed image, and W1, W2, W3, W4, W5 indicating diagonal matrixes for determining whether each group has an element.
 21. The method according to claim 17, wherein the step for computing the restored image comprises a step for approximating the regularization parameter by applying a set theoretic, and it is presumed that the quantization variables of the DCT region are regular in each macro block, and also presumed that the DCT quantization errors have the Gaussain distribution property in the spatial section.
 22. The method according to claim 21, wherein the regularization parameters are approximated as; $\alpha_{VB} = {\frac{{{Q_{VB}f}}^{2}}{{{g - f}}_{W1}^{2}}\quad = {\frac{{{Q_{VB}g}}^{2}}{{{g - f}}_{W1}^{2}} = \frac{{{Q_{VB}g}}^{2}}{\sum\limits_{n}\quad{\sum\limits_{m}\quad{{W_{1}\left( {m,n} \right)}{{Qp}^{2}\left( {m,n} \right)}}}}}}$ ${\alpha_{HB} = {\frac{{{Q_{HB}f}}^{2}}{{{g - f}}_{W2}^{2}} = {\frac{{{Q_{HB}g}}^{2}}{{{g - f}}_{W2}^{2}} = \frac{{{Q_{HB}g}}^{2}}{\sum\limits_{n}\quad{\sum\limits_{m}\quad{{W_{2}\left( {m,n} \right)}{{Qp}^{2}\left( {m,n} \right)}}}}}}}\quad$ ${\alpha_{VW} = {\frac{{{Q_{VW}f}}^{2}}{{{g - f}}_{W3}^{2}}\quad = {\frac{{{Q_{VW}g}}^{2}}{{{g - f}}_{W3}^{2}} = \frac{{{Q_{VW}g}}^{2}}{\sum\limits_{n}\quad{\sum\limits_{m}\quad{{W_{3}\left( {m,n} \right)}{{Qp}^{2}\left( {m,n} \right)}}}}}}}\quad$ ${\alpha_{HW} = {\frac{{{Q_{HW}f}}^{2}}{{{g - f}}_{W4}^{2}}\quad = {\frac{{{Q_{HW}g}}^{2}}{{{g - f}}_{W4}^{2}} = \frac{{{Q_{HW}g}}^{2}}{\sum\limits_{n}\quad{\sum\limits_{m}\quad{{W_{4}\left( {m,n} \right)}{{Qp}^{2}\left( {m,n} \right)}}}}}}}\quad$ $\alpha_{T} = {\frac{{{Q_{T}f}}^{2}}{{{g - f}}_{W5}^{2}}\quad = {\frac{{{Q_{T}g}}^{2}}{{{g - f}}_{W5}^{2}} = \frac{{{Q_{T}g}}^{2}}{\sum\limits_{n}\quad{\sum\limits_{m}\quad{{W_{5}\left( {m,n} \right)}{{Qp}^{2}\left( {m,n} \right)}}}}}}$ Q² _(p)(m,n) indicating a quantization variable of a macro block including an (m,n)th pixel of a two-dimensional image.
 23. The method according to claim 17, wherein a local minimizer of the smoothing functional is a global minimizer.
 24. The method according to claim 17, wherein the regularization parameter indicates a ratio of a smoothing degree of the image and reliability for the original image.
 25. The method according to claim 17, wherein the iterative solution f_(k+1) is represented by; f_(k+1)=f_(k)+β[Ag−Bf_(k)],  A=α_(VB)W₁+α_(HB)W₂+α_(VW)W₃+α_(HW)W₄+α_(T)W₅ B=(Q^(T) _(VB)Q_(VB)+Q^(T) _(HB)Q_(HB)+Q^(T) _(VW)Q_(VW)+Q^(T) _(HW)Q_(HW)+Q^(T) _(T)Q_(T))+A and, β is a relaxation parameter having a convergence property, and computed at the range of ${0 < \beta < \frac{2}{1 + {\max_{i}{\lambda_{i}(A)}}}},$  an eigen value λ(A) of the matrix A being replaced by a fixed value.
 26. An apparatus for restoring a compressed image of an image processing system, comprising: a decoder for decoding a coded image signal, and for outputting information of the restored image, such as the decoded image, a quantization variable, a macro block type and a motion vector; and a post processing unit for including the information of the restored image inputted from the image decoder, for defining a smoothing functional including a smoothing degree of the image and reliability of an original image block unit, and for performing a gradient operation on the smoothing functional in regard to the original image, the smoothing functional including a regularization parameter having weight of reliability for the original image.
 27. A method of decoding a current image using a decoding apparatus, comprising: obtaining, at the decoding apparatus, a pixel value in a current block and at least one adjacent pixel value according to a smoothing direction; obtaining, at the decoding apparatus, a block type of the current block, the block type being one of an intra-coded type and an inter-coded type; obtaining, at the decoding apparatus, a smoothing value of the current image based on the obtained pixel value in the current block and the adjacent pixel value according to the smoothing direction; and smoothing, at the decoding apparatus, a pixel value around a boundary of the current block based on the smoothing value and the obtained type of the current block.
 28. The method of claim 27, wherein the smoothing direction includes at least one of temporal direction and spatial direction.
 29. The method of claim 28, wherein the spatial direction includes at least one of a vertical direction and a horizontal direction.
 30. The method of claim 27, wherein the adjacent pixel value is obtained from a block different than the current block.
 31. The method of claim 27, wherein the smoothed pixel value is the obtained pixel value in the current block.
 32. The method of claim 27, wherein the adjacent pixel value is adjacent to the obtained pixel value in the current block in a vertical direction.
 33. The method of claim 27, wherein the adjacent pixel value is adjacent to the obtained pixel value in the current block in a horizontal direction.
 34. The method of claim 27, wherein the smoothing direction is based on at least one of a whether the pixel value is for a pixel at a boundary of the current block or a pixel within the current block. 